Do you know of a Control Theory for dummies text that you can point us to?.
Control Systems Engineering by Norman S. Nise is a good undergraduate textbook. I don't remember how much Fourier Transform stuff it expects you to already know, but I think not much if any. It most likely does touch on deadbeat control and digital control systems in general.
With a Deadbeat Controller, can you avoid overshoot?.
Almost. Directly from Wikipedia:
The deadbeat response has the following characteristics:
- Zero steady-state error.
- Minimum rise time.
- Minimum settling time.
- Less than 2% overshoot/undershoot.
The way I will write the code, it will be possible for you to design your own controller and edit the code so it replaces the gains that comprise the deadbeat controller. The textbook above will cover a few controller designs that can achieve no overshoot.